Mega-post ahead, be warned... 
A modern scanner from Uniden or GRE/Whistler is a combination of two primary things: a tuner to receive content being broadcast on frequencies, and firmware aka software to control the tuner/decode the audio (in analog or digital format) and provide it to the audio circuit so you can hear it.
An RTL stick is basically a scanner missing the software - it's a tuner that offers pretty much exactly the same basic functionality as far as receive content being broadcast on frequencies. The software component is provided by applications, programs, and software running on a computer that can allow for more functionality and true "hands on" control of most every single aspect involved, far more control than you'd get with any modern scanner. The software used can turn an RTL stick - depending on the complexity and feature-set of the software itself - into a communications receiver and not just a "scanner" but you still have that option as well (input a set of frequencies and then monitor just those frequencies in sequence, like a scanner does).
With RTL sticks - and by that I mean the most common models that use the RTL2832U chipset from Realtek coupled with the R820T tuner from Rafael - there is also the Elonics E4000 tuner but it's much rarer and more expensive nowadays because of the rarity as Elonics is no longer in business and they only offer a wider frequency range for reception - it is exactly what it purports to be: a "cheap USB TV tuner" that was designed to work with the European DVB-T digital TV format which will soon be replaced by something else (from reports). Someone discovered that you can use these sticks as radio tuners forgoing the actual TV/video aspect if you use the right drivers and the right software to make use of them in this respect.
Now, while they ARE very capable receivers, they obviously require that software to make use of them, hence the still somewhat recent "explosion of interest" towards SDR in general. The interest isn't because of Software Defined Radio which has been possible for many years now, the interest is solely because these "cheap USB TV tuners" give you the ability to do SDR type monitoring
with extremely low cost - that's the primary draw. Sure, we'd all love to have a nice wide bandwidth USRP device from Ettus sitting on our desktops tuning in everything we can but very few of us are capable (or willing) to toss out several hundred bucks for such a device, or even a few grand for the highest end models.
To put it bluntly: no, you won't get the same exact experience with SDR and RTL sticks as you do with the BCT-15X or any modern base/mobile/handheld scanner. It takes a bit more effort to get the same or similar functionality in the long run, and obviously more hardware and software as well: a computer of some kind, the RTL stick(s), the drivers to make them recognizable to the software which is used to make them functional, and of course the potential additional need for more software to do trunking capabilities as well as yet another piece of software to decode the digital communications protocols now gaining traction in the radio communications world of today.
With SDR# (and potentially other SDR programs as well) it is possible to create a database of frequencies, even groups designated for particular purposes, and then "scan" the frequencies assigned to said group just as a modern base/mobile/handheld scanner would do, sure. There's a plugin for SDR# called Frequency Manager + Scanner plugin which does precisely that and I use it myself and have no issues at all with it. I can assign delay times to stay on a given frequency (to follow the comms), I can assign specific signal strengths to stop on (this is different from squelch, for the most part), and other aspects per group as required.
So yes, again, it's possible to use RTL sticks as "scanners," most definitely - it just takes more work to make it possible. And again, today's modern scanners, even the most current ones from Uniden can only decode P25 in terms of digital protocols, both Phase I, X2-TDMA, and the newest variant which is Phase II. Any other digital protocols like DMR/MOTOTRBO (gaining a lot of popularity very very fast in the business radio communications areas) and NXDN (also gaining popularity, especially with railroad operations) and now even D-Star (somewhat popular with Ham radio operators) cannot be monitored directly by any modern scanner but you can handle them using software like DSD or DSD+ (D-Star voice support was just recently added to DSD and it's still in progress too). Of course DSD and DSD+ can handle P25 Phase I and X2-TDMA - those decoders can't handle Phase II yet but there's always the hope that support will be added in the future.
The issue then becomes "Ok, I want to monitor <whatever protocol>, do I want to do it a) using my actual scanner and a discriminator tap fed into DSD or DSD+, or b) using RTL sticks doing the same thing with SDR software and DSD or DSD+?"
See the one thing there that remains the same between either a or b?
You still have to have a computer involved at some point to decode those digital protocols... even with your BCT-15X.
So you have to decide something: do you want to (or need to) monitor strictly analog systems (which your BCT-15X is perfectly capable of doing without a single issue), or do you want to be able to monitor analog
and digital systems like P25 (at the minimum Phase I and X2-TDMA if they exist in the areas you want to monitor), DMR/MOTOTRBO (in use most everywhere to some degree if you look for it), NXDN (not nearly as widespread but still in use in some areas), or even potentially D-Star (very limited use and it would require the dev build 1.7 of DSD to monitor at this time), and so on...
If everything you want to monitor is analog, stick with your BCT-15X since it's a known thing and you're familiar with it and traveling with it. If however you want to try some new things and learn something (keeping on top of current trends, etc) then adding an RTL stick or two is a great idea in the long run. As scancapecod said above, it's entirely possible to do both in the long run as an RTL stick or two along with the cables, antenna(s), etc are all very small and don't typically take up much space at all in a laptop bag.
And, another benefit: with an RTL stick added into the situation, you'd be able to monitor two systems at one time if you're really good at multitasking.
Last last tip: forgot to mention this earlier but if you do have a laptop on the go (pretty sure you do) and you have intentions to get into RTL, I highly recommend getting an additional cable - a USB extension cable at least 3 feet long, maybe 6 would be better. The reason is to get the RTL stick out of the USB ports on the side(s) of your laptop which put them in a very fragile position should you drop it or potentially fall asleep with it and then roll over snapping off the USB stick at the point of connection. You'd be amazed at how many people get those 3G/4G wireless sticks from various cellular providers and they leave them plugged in all the time - at least till they drop the laptops or do just that, roll over on them when they fall asleep on a bed or couch and end up with a damaged stick and even worse a dead USB port on their laptops in the process.
Having the extension cable won't necessarily protect the USB port itself if such an event happens, but at least you save the stick from being destroyed in the process. Just a suggestion...
