I originally ordered the Boston Acoustics Trio because of better features but due to a couple of issues (details below) decided to switch to the Wave. While I had both units, I did a side by side comparison, and here is a summary:
Sound Quality: Both the Trio and the Wave sound great. Listening to the same radio station and CD in both, the sound is different and IMHO the Bose sounds better. Especially in higher frequencies and lighter tones. Some may like the Trio better. But the difference is not likely to be a deal breaker for either.
Sleep feature: Both units allow a programmable sleep time (up to 90 min). When it is time to turn off, the Wave gradually lowers the volume and turns off. The Trio suddenly turns off at whatever volume it was, which can be jarring. Bose wins.
Controls on Unit: Trio controls are nice to use, and most people will not need the manual for common tasks. The Wave has no buttons on the unit itself, every control is through the remote. If you buy the iPod dock, you get an additional remote for the Wave and then one can leave one remote near the unit. But still, the lack of a Snooze button and CD eject button on the Wave is annoying. And one has to worry about not loosing the remote or having a dead battery one day. The Trio definitely wins.
Remote control: Comparable features on both. Bose does offer an optional bigger premium remote with back-lit buttons.
Radio: The Trio shows radio station names and the name of the currently playing song. The Wave only shows the station frequency. Wave does have one more pre-set memory location. Boston Acoustics wins.
iPod: The iPod dock was free with the Wave at the time of this writing (through Bose) and deeply discounted with the Trio (through Boston Acoustics). The docks work on both, but are only mediocre in terms of the amount of control over playback one gets from the remote. The Trio dock does allow for the alarm to be set to wake to iPod. The Wave dock needs a separate bulky power adapter while the Trio dock gets its power from the same wire that connects it to the Trio. Both do charge the iPod. Trio wins.
Alarm: The Wave has one alarm, which cannot be programmed for days of the week. The Trio has two alarms each of which can be set for all 7 days, weekdays, or weekends. Trio wins. (BUT, the Trio seems to have a bug, also noted by some reviewers for Trio. I set both alarm 1 and alarm 2 on the Trio. Alarm 1 was set for an earlier time and it did go off at the set time. The Snooze worked. But when I turned off the alarm using the correct method, two bad things happened: Alarm 1 automatically reset to 12am, Alarm 2 turned off and did not sound at the set time.)
Wake to: The Wave allows the alarm to be set to CD or Radio. The Trio allows CD, Radio, iPod, or a tone alarm. Trio wins.
Battery backup: Both the Trio and Wave remember the time, alarm, and radio presets in case of power failure. Neither will sound the alarm if there is no power at the time the alarm is supposed to sound. Its worthwile to note that many cheap radio alarms have a backup alarm on batteries that sounds even if there is no power.
Clock: Neither adjusts for daylight savings. The time display IMHO is better on the Bose and easier to read, though the screen on the Trio is higher resolution. Both allow for changing the display brightness. The automatic brightness change on the Trio is jerky and not pleasant to look at when its changing. The Bose brightness change seems imperceptible.
Looks: This is very subjective. I liked Bose better. More importantly, my wife liked Bose better and she has a good aesthetic sense. Maybe that's why she married me :-)
FM Antenna: The Wave's FM antenna is part of the power chord, so no need to extend and hide an additional wire. The Trio has a separate wire for the FM antenna. Bose wins.
AM Antenna: Hidden for the Wave. Exposed as a twisted wire for the Trio, which for me was damaged on delivery. Bose wins.
Price: Bose spends more on marketing and customer service. They have local stores where one can experience the products in person. As expected, Bose is more expensive.