I've been flying the 109 as my primary plane for awhile now, I like it a great deal but still have lots of trouble with the tater gun.
Outmaneuvering other fighters isn't difficult with the 109.
As far as flying in the vertical it basically means that whenever you get the chance, force yourself and your opponent to climb. The 109 K4 will climb at ~4,000FPM with WEP, the G-14 with Gondolas slightly under that.(I use Gondolas because I can't hit the broad side of a Lancaster. I don't turnfight enough for them to be really detrimental.)
The 109 can also maintain this climb rate at close to 200 IAS maybe even a little less. So when the E of a dogfight gets real low its a great advantage to pull out a steep climb with the wep and leave most fighters low and slow.
As far as practicing with the 109... find a FT arena and start off slowly with BnZ tactics until you get a feel for how she climbs and dives, then start expanding into small turn-fights. The problem with the K4 is that when most people see it start to maneuver it paints a bull's-eye on the plane.
I've been able to turn with higher-end spits, la's, and other such aircraft for longer than the opponent thought possible.
If I could actually use the tater gun I'd probably land 20 kills in her per flight.
But the G14 will maneuver comparably with the K4 and allow you to use a 20MM with a higher rate of fire which makes hitting enemies alot easier, at least until you're used to the nose-gun then switch off to the 30MM.
What it sounds like you're doing is pulling too steep to engage someone who started the fight with more E than you.
The best solution I've found to combat that is to follow them up at a lesser climb rate, wait for them to nose down towards me and then violently maneuver to their down or up.
Either they'll red out trying to keep a firing solution, or they'll stall and snap-roll trying to pull up too hard.
Then you use the 109's superior acceleration to level off rebuild some speed and re-engage at a higher altitude than before. Because if you force them into a vertical HO and dodge it, they'll have to burn alot of the speed and E they just gained from diving to maneuver back around to you.
When used right and with a little luck its a good way to equalize E states, especially against guys with large Alt-advantages. However most smart opponents will simply move out 3-5 K before swinging back around to try for you again. Even then though, it will give you critical minutes to get up to a decent fighting speed.
The 109's dream altitudes are between 5-20K, I think. So the higher you can drag most enemy fighters the better your ship will perform. But really high alts you want to stay away from, thin air and the 109 don't mix.