I find it interesting that one company Ruger has two very different .22 semi autos. I have had experience with the Mark IIs but never with the SR22s so I would like to know which is better?
"Better" can objectively differ by application. Your context below is "teaching new shooters," in which case, the Mark IV is the "better" of the two.
A RECENT ANECDOTE OF MINE AS A DIRECT EXAMPLE:
A student in one of my Basic Pistol classes last fall was struggling REALLY badly to complete the qualification shoot for the course with her SR22. She'd owned the pistol for a couple years, but I noted she immediately was struggling even during the bench-support shooting string. By the longer range standing fire string, the wheels had completely come off. She was struggling to make contact on the 8 1/2" x 11" printed page, let alone the correct target circle within the page. After failing to qualify on her first time through on the Level 1 (5 shots per target, 4 targets of 4" dia, at 10ft), I offered one of my Mark III pistols for her to try. 60 shots later, she'd cleared all 12 targets (5 shots x 4 targets at 10, 15, and 20ft) without a single shot going astray.
Or are they so different from each other as to not really be comparable?
It's very easy to compare the two, despite their vast design differences, when you put them in a specific context - i.e. "teaching new shooters." So when you start comparing attributes for two in the context of instructing new shooters:
The Mark IV has a longer barrel and longer sight radius, which is an advantage for shooter forgiveness. The Mark IV is drilled & tapped for an included weaver rail, which would allow the installation of a red dot site, which is the easiest sight design for a new shooter to adopt (put the dot on the target, pull the trigger while the dot is on the target), offers a more precise aiming system than the conventional sight blades. and also offers a new shooter a more comfortable "open view" of the target compared to a 6 o'clock hold with iron sights. The trigger in the Mark IV is better than the SR22. The extra length and weight of the Mark IV offers increased stability with less muzzle bobble on target. The extra weight also reduces the felt recoil impulse; not that the SR22 has high recoil, but it has considerably moreso than the Mark IV.
The only advantages I have ever seen, minor as they are, for the SR22 are: 1) the diminutive size of the SR22 can be less intimidating to some of the more timid shooters, and 2) the lighter weight of the SR22, while less stable, can be an advantage for the smaller and weaker new shooter. So I often see the "quieter" women and younger guys in classes pick up the SR22 out of my rack, just as they might be drawn to a less intimidating LCP too - both being a poorer choice than a Mark IV.
If that is so then which on would be the best for teaching new shooters?
Read above - the Mark IV all the way.