While I assume Aggressor is the more luxurious of the two (never been on an Aggressor), I also believe it's smaller in terms of space. The ships are the same size but the layouts are different. I looked at both last May - we chose Explorer for a couple of reasons. (one was $500 off)
Some differences I noted:
Explorer has 5 of their cabins on the main deck and two VIP cabins on the upper deck. This means that the main deck cabins (ours) had two windows. All the Aggressor cabins seem to have a rectangular porthole only. And all are one deck below the main deck.
If you look at the ship pictures/descriptions, all the Aggressor cabins except one have double bunks with a single on top of them. All the main deck/upper deck Explorer cabins either have twins or a queen bed - only the three downstairs are bunks. All also have enough room for a small desk - the queen cabins even have a dresser IIRC. Ours had a regular sized nightstand between the beds and drawers under the bunks. And an adequately sized bathroom. (for a LOB)
Aggressor has a small TV in every cabin. Explorer it's only the VIP cabins and the two front main cabins afaik - ours didn't. We had the cabin next to the galley so we always knew what was for dinner.
I would expect the dining is a little nicer on the Aggressor - at least from the pictures/menu. But Stan the cook on the Explorer is almost legendary - excellent food all week. (Ask him if he's been diving yet - he won't have...lol) Almost every meal was buffet style with the crew serving dessert.
I'm sure it's the same on both boats but the crew was exceptional. Well beyond just working for tips. Tim ran the boat and Sandy his wife is the Purser. They're good people.
Explorer has an extra deck also. Look at the ship layouts - Aggressor's main dining area/lounge is on the main deck with the dive deck behind it - bridge in front. Explorer has 5 cabins, the galley and dining area/lounge on the main deck with the dive deck behind it. The two VIP cabins are upstairs and have their own stairs to the lounge. The bridge area is on the upper deck also. Behind that is a large open sun deck area and on top of that is the flybridge, covered permanent awning with tables, benches, a small mini-bar, music and a bbq (not used our week) The flybridge is very pleasant, we did SI's up there and I slept up there twice.
The diving is basically the same. At least twice during our trip we saw Aggressor on the next mooring over. French Cay was the best, West Caicos was very good and NW Point was a little disappointing. We saw sharks, turtles, barracuda, stingrays, eagle rays and a few big lionfish off French Cay - one day all of them - on three dives.. West Caicos was a lot of turtle and some grouper - lots of stingrays in the shallows near the boat - and lots of macro in the coral heads. One of the photographers on our boat shot some Nat. Geo. quality stuff there. Also there was a daily drift dive while there. NW Point off Provo was less memorable - a year later.
One thing I've never seen before - Explorer vents the compressor heat up through a vent in the middle of the divedeck and has a pole above it for wetsuits to dry quicker. I don't dive in a wetsuit but my morning t-shirt was always dry by mid-afternoon. Dive deck was a little crowded but we had a full boat. And you can either jump off the side (about 6') or walk down the stairs to the dive platform area where there's two hot water showers for your return. Really hot water, they had to turn it down mid-week. At night the crew has hot water to pour down your suit.
Another consideration for your timeframe is that Explorer does the Whales of the Silver Banks trips from the last week of January thru April. I believe those are primarily whale-watching snorkel trips - I'm not sure how much diving gets done then - if any. Explorer showed us a promo video onboard - it was all snorkeling or following them from their tenders. Also those trips leave from Puerto Plata in the Dominican Republic.
I believe Aggressor has a similar schedule based on the
trip report on their website.
One other thing is that Explorer only makes the run to Grand Turk certain weeks. It's not really apparent until you look at the availability schedule in detail, I was a little disappointed as I wanted to do the GT wall dives.
I found a good Explorer trip report with pictures last year b4 we went:
Saudio's Trip Reports