[RPG] What does increased caster level affect

The answer depends on whether or not either or both of them has shield (or similar) active.

Case 1: Neither has shield active

With no shield spells in play, Overpowering Missile does not come into play at all. Reflective Shield does not replicate the effects of the shield spell, and only refers to that spell when it is active on the other guy.

Instead, the situation is identical to if both of them had an infinite version of spell turning active: a resonating field is created, and you have to roll on the chart.

Case 2: One has shield active

The one with shield active has his own missiles, turned by his opponent’s Reflective Shield, negated by his shield spell. The missiles turned by Reflective Shield are explicitly negated by shield or similar, which trumps the caster’s own Overpowering Missile feature (specific trumps general: his magic missiles generally ignore shield, but Reflective Shield specifically says the turned missiles don’t ignore shield).

The one without shield overcomes his opponent’s shield due to Overpowering Missile, but then the magic missile is turned by Reflective Shield. He has his own Reflective Shield, so you get the same resonating field as you did in Case 1, but only on his turn rather than for both their turns.

Case 3: Both have shield active

The shield on each of them negates their own turned magic missiles, and so a resonating field never occurs. They are literally burning spell slots to no effect.

To tilt the frame slightly, instead of increasing your caster levels to ridiculous heights, you can try to avoid getting your spells dispelled by just becoming immune to spells that dispel magic. While many spells dispel magic, unless the DM is Dumpster-diving to deliberately overcome your shored-up defenses, you only really need worry about the 3rd-level Sor/Wiz spell dispel magic [abjur] (PH 223) and the 6th-level Sor/Wiz spell greater dispel magic [abjur] (PH 223).¹ The basic items that help do this:

• The ring of counterspells (DMG 230) (4,000 gp; 0 lbs.) counters once the spell that's cast in it after which it can be reloaded with the same or a different spell.
• The ring of spell-battle (Magic Item Compendium 127) (12,000 gp; 0 lbs.), in addition to other effects, grants the wearer 1/day the ability to redirect a spell that the wearer's identified that's cast on him at a different target within a limited range.
• The magic weapon special ability spellblade (Player's Guide to Faerûn 120) (6,000 gp; 0 lbs.) is keyed when created to one specific spell (like dispel magic or greater dispel magic but not both), and when that spell is cast upon the weapon's wielder he can either redirect the spell to the originator or have the spell dissipate.²

Note that of these only the ring of spell battle can, after its fashion, defend against area dispel effects.

Other similar magic items likely exist—as do shenanigans (like finding someone with the feat Craft Contingent Spell (Complete Arcane 77) and paying him to ensorcell you appropriately)—, but the above list probably holds the most convenient and palatable solutions.

¹ Other spells that dispel magic include (but by no means are limited to) the 2nd-level Sor/Wiz spell arcane turmoil [abjur] (CM 96), the 2nd-level Sor/Wiz spell dispelling touch [abjur] (Player's Handbook II 110), the 8th-level Sor/Wiz spell blackstaff [trans] (Magic of Faerûn 81), the 8th-level Sor/Wiz spell chain dispel [abjur] (Player's Handbook II 106-7), and the 9th-level Sor/Wiz spell reaving dispel [abjur] (Spell Compendium 169-70).
² Many weapons can be wielded—often simultaneously—an not occupy a creature's hands. I suggest multiple surprise weapons (Complete Scoundrel 109-10).