I have used Speedplay pedals for 19 years now, and I love them. I would also recommend that most beginners avoid them.
This Cyclingtips article appears to back me up. Speedplays have small bearings, and they need to be serviced with a grease gun annually. This can be a little messy, as the old dirty grease will get pushed out on the inside of the pedal. Separately, the cleats need to be lubricated periodically, perhaps monthly.
Furthermore, the cleats need to mount flat to your shoes, and I have had some issues getting the base plate completely flat on some shoes despite using the manufacturer-specified shims. (NB: this varies by shoe, and most users shouldn't encounter this issue, but I doubt any SPD or Look user encounters this issue at all.) Speedplay cleats may also be more vulnerable to fouling by dirt, which can affect you if you step in mud, sand, etc.
I bother with Speedplay because you can adjust the Q-factor using the cleat mounting screws, and if that’s not sufficient, multiple axle lengths are available for further adjustment. Also, some reviewers like Josh Poertner of Silca have suggested that being smaller, they are slightly more aerodynamic than other pedal systems. Neither advantage is essential for all users. The aerodynamic difference is measurable but slight; consider that professional road cyclists would probably switch en masse if it were a large difference. At the time of writing, Speedplay sponsored two World Tour-level (i.e. top tier) road cycling teams and several second-tier teams, plus a few individual road cyclists (including former professionals). However, Dan Empfield of Slowtwitch.com documents that Speedplays are very popular among top-level triathletes. He also explains the benefits of the pedal in some detail here.