WGBH has the better signal. In fact, it's the strongest FM signal in Boston, grandfathered at 100,000 watts at apx. 650 feet, while WBUR has a standard Class B signal, 12,000 watts at about 1000 feet, similar to most Boston area commercial FM stations.
WGBH is, on paper, the best signal in town. In reality it's not...the relatively low height of Blue Hill means that GBH has trouble getting good reception in downtown and, to some degree, in parts of Cambridge shadowed by downtown. Remember that GBH was trying to move to the Newton/Needham tower cluster a few years back? What stopped them was, IIRC, that they wanted to keep their equivalent Super B power levels (98kW, but de-rated for the extra height) and the FCC said they'd have to drop ERP to be an equivalent Class B (50kW) like everyone else.
Worcester is the second-largest city over Providence by fewer than 3000 people, and that's just the official city borders. The Providence "metro" is MUCH larger than the Worcester "metro."
WICN is not audible much east of Framingham due to first-adjacent WZBC and co-channel WSMA. For years I've suggested that WICN should try and partner with WBMT and put the jazz on when the kids aren't there. It wouldn't get into Boston, but it could; WBMT could move to the old WBOQ tower in Gloucester and move to 88.5 with about 3000 watts or so. It'd be a decent rimshot into Boston then and still serve a lot of the north shore nicely. Put that together and you'd have a decent full-time jazz presence in Boston in the first time in years.
Diane Rehm has spasmodic dysphonia, that's why her voice seems so strained. I believe she gets one of the "standard" treatments of botox injections to relax the vocal cords every few months: you'll hear her get gradually worse, then she disappears for a few weeks with a cadre of guest hosts (many of whom are excellent, I might add) and then she comes back sounding much better, and that gradually fades off, etc etc etc. IIRC her contract was up next year but it's already been renewed for another five years by NPR. Diane might be hard to listen to but she does get good political guests, and she's usually not afraid to cut someone off at the knees, either. Certainly the show is VERY popular in a lot of regions. Not so much Boston, but a lot of the rest of the country.
As for which is better, WBUR or WGBH, I'm obviously biased against WGBH but I think WBUR will always have the edge because WGBH has both TV and radio, and TV always takes priority there. WGBH is the source of about 1/3rd of all PBS TV programming, so it's clear which side of the house the bread is buttered on. WBUR also has a nearly 20 year head start on establishing themselves as the *local*, *NPR* and *news* station in town.
As for newsroom sizes, I think WBUR's is bigger but it's a bit misleading as WGBH has
The World and their news staff is (or at least was) pretty huge. Maybe call it a draw?? OTOH, WBUR just inked a deal with NPR for
Here & Now and that's a collaboration so it's bringing more NPR resources into WBUR's newsroom.