Quick recap/ tl;dr - 1. Rdm is not BLU. Blu makes sacrifices to be better in some areas while weaker in others. RDM should be all things out of the box. 2. RDM just needs a little melee loving to make it what the job is meant to be.
P.S. to those "Go be BLU then" people... spell farming for hours on end? No thanks. I'll stick to buying them like i have for years and keep playing the only class i love.
As someone with a fully blinged out BLU and RDM (melee and mage varieties) I'm able to compare then two because they both fill the exact same position. If you need pure damage you bring one of the specialist melees, if you need pure healing / support / crowd control then you bring one of those guys. RDM / BLU (melee varieties) are for when you need damage, support and crowd control. In this regard BLU stomps all over RDM, picks it up dusts it off then stomps all over it again. This is mostly due to SE showing BLU lots of love in both the damage and support departments while completely ignoring RDM.

Ex:
Melee BLU (has TA / DWIII natively thus can go /WAR for bergressor / DA / ABI) access to much better WS's and gear selection. Can self SC and use CA and / or Efflux to land 2~3K+ physical damage spells of whatever damage type is needed. Can self Haste / Refresh

Melee RDM (must go /NIN to contribute meaningful damage), limited access to WS's without Almace, limited and restrictive melee and WS gear options. Tons of self buff mitigate this penalty somewhat. Can nuke but bad time vs damage ratio.

Support BLU (while being /WAR) M.Fruit is a cheap cure IV, P.Embrace is a more expensive backup cure that buffs people's attack. White Wind is Curaga III~IV basically. WoP aoe Erase (BY FAR THE MOST IMPORTANT SUPPORT SPELL). Stun spam if needed (HB / SL / TS / WoR). And if all that wasn't enough, BOTH light and dark based aoe CC (Sheep / Flower). Can aoe Haste once per 10m with a 5m haste (longer if merits / gear permits), useful before fights or during NNI.

Support RDM (while being /NIN) Cure III~IV for cures, Regen II for HoT. No status healing and only ST CC's (bind / grav / sleep I / II). 5% More -def then BLU (if they even bother with FR) which is easier to use. Can Haste / Refresh others.

Support RDM (while /SCH) Cure III~IV for cheap cures, Regen II for HoT. Can remove the major status healing but no cheap aoe erase. Haste / Refresh as usual. Slightly better nuking thanks to DA, but still poor when compared to melee.

Seems kinda lop sided huh? Any situation where I could in theory bring a "Melee" RDM I would be better off bringing my BLU, and any situation where I would bring a "Mage" RDM I would be better off bringing my WHM, BLM or SCH. This has left literally zero positions for a RDM to actually exist in FFXI, all they do now is go around making video's while soloing some monster without TH that could better be killed with a group of 3~6 with TH.

Now don't take this as a rant against BLU, I absolutely love my BLU. It's one of the few jobs SE actually got right and hasn't screwed up *yet* (knocks on wood). I believe SE should buff most if not all jobs to the level BLU is at, in usefulness if nothing else. BLU is a shining example of what a "hybrid" job should be, it can deal sufficient quantities of damage to warrant serious discussion (but not as much as the specialists). It can heal enough to warrant inclusion in low man group activities. It can apply enough crowd control to make it a vital asset in any group. And it does all these without stepping on the toes of the specialists jobs. BLU's got enough flexibility that it can assume nearly any position in a group, multiple times while leveling to 75 (in those days when we used to kill colibri) I've main healed partys on BLU (no healer lfp). BLU's only weakness is that because it's not as good as the specialist jobs in any one thing, it's not preferred for big 18 member alliance mega boss fights which are basically Legion and Voidwatch.

So for your comparison, it's more like RDM is the straight C student with the BLU being the A student who is also a starter on the all star football team while playing in band. The RDM is the guy who you hang out with when you got nothing else to do and just shooting the sh1t about the world. The BLU is the guy who you actually want on your school's competitive teams.