Reputation is a nebulous quality which is difficult to measure. The only concrete data with regards to reputation that I'm aware of is that provided by QS World University Rankings, which is
partially driven by survey data - where they send surveys to academics and employers around the world and essentially say, "Do you rate this uni?" (I'm paraphrasing.

)
Looking at that data (
source), for Employer Reputation Glasgow scores 69.6 whilst Queen Mary scores 72.5 - so not much in it. For Academic Reputation Glasgow scores 71.9 whilst Queen Mary scores 80.5. Note, however, that a better reputation may just mean better marketing / Public Relation departments.
In terms of future job prospects, I like to use the data from the Destinations of Leavers from Higher Education Survey, as published on The Uni Guide.
From that we can see there, sixth months having graduating with a Law degree from Glasgow (not necessarily your specific Law degree), 99% are employed or in further education. However, only 50% are employed in a role where degree was essential or beneficial, with 15% being legal professionals and 11% being legal associate professionals. (
source)
By contrast, sixth months having graduating with a Law degree from Queen Mary (not necessarily your specific Law degree), 93% are employed or in further education. 64% are employed in a role where degree was essential or beneficial, with 26% being legal associate professionals. The proportion being legal professionals doesn't feature in the top three top job areas of graduates. (
source)
For me, none of that information is particularly compelling one way or the other. There's plenty of other information on those pages which might help you though (including median earnings of graduates, in the first, third and fifth year after graduating - from the Longitudinal Educational Outcomes dataset - and student satisfaction data from the National Student Survey) .