Tiers does exist, and are used to differentiate Tech1 ships from a same class. While being the same class, they fill diverse roles (mining ships, pew-pew ships), and their tier value allow you to find their exact roles (if you're to lazy to read their bonuses)...
Here is a french related forum thread, illustrating my point. (Translated! Traduction is probably innacurate, due to french being my natural langage. Feel free to edit if you see any mistakes.)
While being weak, frail, limited, frigates offset those points with unbeatable prices (always less than 300,000 isk). Because they are able to fit a few weapons, a propulsion module and / or a scrambler, they are always useful, would the pilote be a vet or a newbie, in PvP or PvE.
There are 6 variants that exist in almost any tech 2 more powerful and specialized version:
tier 1 frigates : Tormentor (A), Bantam (C), Navitas (G ) & Burst (M) are optimised for mining. They are useful only for miner apprentices before moving on to a bigger ship. They are available on the market at an unbeatable price and you receive one at the beginning of the 10 missions from the early industrialist/trader career
These frigates have no tech 2 equivalent.
tier 2 frigates : Executioner (A), Condor (C), Atron (G ) & Slasher (M) are light, fast and very affordable. By the way, their price is their only real interest, except maybe to start in PvP. One of them is given at the beginning of the 10 missions fighter career.
Tech 2 version of these vessels gives Interceptors.
tier 3 frigates : Magnate (A), Heron (C), Imicus (G ) & Probe (M) have small exploration bonuses. Note the Probe (M) which has a great bonus to cargohold which allow him to be a good small transport ship or Cyno alt. Also note the Imicus (G) is a very good offensive frigate with its drones.
Tech 2 version of these vessels gives Covert Ops.
tier 4 frigates : Crucifier (A), Griffin (C), Maulus (G ) & Vigil (M) have a greater interest, particularly in PvP. Indeed, these vessels are specialized for ewar. They are certainly far from having the power of a Recon but they can get their game on a battlefield. Note the notable exception of Vigil whose interest is not his ability but his ewar speed interceptor role.
Tech 2 version of these vessels gives EAS.
tier 5 & 6 frigates : Inquisitor & Punisher (A), Kestrel & Merlin (C), Incursus & Tristan (G ), Breacher & Rifter (M) are all fighting frigates. These are generally the best tech frigates 1 in most combat situations. Some of them are particularly good and still used by veterans.
A tier 6 frigate is given at the end of the 10 missions of the fighter career.
The tier 5 provide the foundation for SB and those of tier 6 those of AS (except for Gallente which are reversed).
The Tier value change the required commandship skills levels requirements.
The Tier value also impacts the manufacturing needs. Higher Tier ships requires more ores.
Tier values change manufacture time, BPO copy time, probability of BP invention success, etc...
I believe some more points to be also influenced, like survivability (a Punisher is sturdier than an Executionner, for exemple), or effectiveness, but i wont try to produce the whole differences list, it would take a while, and you already have the main points...
Feel free to edit my post if you think i missed something essential.
Unfortunately, it is difficult to give you a definitive answer given that situations vary so much in EVE, all you can do is try to stack cards in your favor.
Some things to consider though:
Interceptors survive on speed, get a Warp Scrambler, hopefully you can use it (possibly overheated) to turn off their MWD which will lend you a huge advantage.
Remember Lasers do EM and Therm damage only, tank for it
Amarr are armor tanks, which makes them vulnerable to Kinetic/explosive. He probably doesn't have that much to plug that hole.
Personally I would look into destroyers, they hit hard, recently were buffed, and fit with tracking mods can probably hit the quick bastard.
Failing that, get friends, or starve him until he goes away.
Fly Safe!
Best Answer
The main skill that affects power grid is Engineering, but there are several others that affect the PG requirements of specific modules or rigs:
The main implant that increases PG is the Inherent Implants 'Squire' Engineering EG series, which provides a 1-6% increase in total powergrid. The 1% version is extremely afforable even if you lose your pod often, but one significant drawback is that the implants for powergrid and CPU use the same slot, so you can't upgrade both with implants at the same time.
The Genolution Core Augmentation implant set is another way to boost PG. The CA-1 provides a 1.5% PG increase, and together with the CA-2 it also receives a 50% set bonus. You can fit these implants in addition to the Squire Engineering one.
There is also the Zainou 'Gnome' Shield Upgrades SU implant series which reduces the PG requirements of modules that require the Shield Upgrades skill by 1-6%, but that is a rather niche benefit and probably only useful in very rare cases.
There are several modules that increase power grid: