Yes. Element length = the resonate frequency. Antennas work best when they are cut to the proper length of the frequency you want to listen to.
If the antenna is an All-Band 25-1300MHz antenna is the length just personal preference?
See above, resonate frequency is what matters. Longer antenna elements are resonate at lower frequencies. Shorter antennas are resonate at higher frequencies. There are ways to combine elements to make them resonate a different frequencies.
Do keep in mind that if the antenna is not resonate at a specific frequency it does not create an "RF brick wall". The antenna will work, just not as well.
Does performance vary by length? From 1 2/3" up to 17" all specify All-Band coverage from 25-1300MHz.
Depends on where you are trying to listen. A 1 2/3's inch tall antenna is probably going to receive _something_ if the signal is strong enough. It'll likely work better at higher frequencies. I can tell you that a 1 2/3" antenna is going to absolutely suck eggs if you are trying to listen to 25MHz. Unless you are sitting on top the the transmitting antenna, you probably are going to have issues.
A 17" antenna is going to be resonate in the VHF High band. It may work well at higher frequencies too. It'll likely work better than the 1 2/3" antenna trying to receive near 25MHz, but still is going to be a compromise.
Logically, I would think the longer length would get better coverage and clarity,
Yes, no and maybe. There is a thing called "capture area" that sometimes can be dragged into this. This suggests that a longer antenna will pick up more signal. Resonance still rules, though. Other things come into play, the ground plane under the antenna, local noise floor, and maybe a million other random things.
but if I can get the same performance from an antenna that is 1 2/3" long why would I want one 17" long?
You will not get the same performance from the shorter antenna on the lower frequencies. It -might- work better up around 1300MHz. This is called "marketing hype". If you chose to believe the hype, let me know, I've got a great deal for you on a nice bridge sitting on some swamp land in Florida.
BTW this is for a hand held scanner that is mostly used at home and stationary, however, on rare occasions I may use it while in my car and possibly even on my boat.
Hand held radios are limited by the ground plane they present to the antenna system. I'll tell you this, it doesn't look good.
You can buy hand held radios that will transmit and receive down past 30MHz, but they don't work well due to the limited ground plane and the realities of fitting a resonate antenna onto a hand held radio.
You'd do much better by using an outdoor base station antenna for all your home use. You will pick up a whole lot more stuff to listen to. It'll cost some money to do it right, but if you are serious about hearing radio traffic from more than a few miles off, it's what you really need.
Inside your car is a big issue. A car is a metal cage often with metal filmed tinted windows. All this works really well at blocking radio signals. Sure, it'll work, but no where near as good as if you install a mobile antenna.
The boat really depends on the design. If it's a fiberglass boat or an open aluminum boat you will still see much better performance from an external antenna. A 17" antenna on the hand held will probably work. In fact, 17 Inches is pretty dang close to being resonate on the VHF marine band.
Don't shortchange your system. You can buy a $15,000 receiver and put a $10 antenna on it and it's going to perform like crap. Take a $100 receiver and put a $15,000 antenna on it and it's probably going to work really well.
I've got a number of radio systems at work and it's very realistic to spend as much on the antenna(s) and feedline as I spend on the radio repeater itself.
If you take a hand held scanner and stick a cheap antenna on top you will be disappointed. Invest some money in a good antenna for your home and car and you'll have a much better experience.
This is -exactly- why police cars, fire trucks and ambulances will almost always have a mobile radio with a properly installed mobile antenna even though the officers/firemen/EMT's will often have a hand held radio.
You can design a two way radio system to work well with handheld radios inside buildings and cars, but it takes a lot of money. Chances are that the systems you will want to listen to are not designed for that.