I thought it might be interesting to compare two different strategies for getting Sonos music in your backyard. Both strategies have their positives and negatives, and what works for you is going to depend on your particular situation and needs.
In order to compare them fairly, let's consider a relatively small space where a stereo pair of speakers will cover the area nicely.
Cost - Advantage MOVE
The cost for two Sonos MOVE's is $800. The AMP costs $600, leaving $200 for a pair of speakers, speaker wire, and potentially installation costs. Although you could put in a system for under $800, it's hard to believe you'd get the equivalent sound quality of a pair of Sonos MOVE's. One thing to consider is that you'll like need a shelf or table to place the MOVE's on, which you may or may not already have, that will add costs to the MOVE.
Audio Quality - Advantage MOVE
This is going to be subjective, and will depend on the quality of the passive speakers used with the AMP. However, if using passive speakers that will keep the cost of the speaker + AMP near the cost of two MOVE's, it's unlikely you'll be able to match the MOVE's sound quality.
Ease of Installation - Advantage MOVE
The MOVE only requires the basic Sonos setup. Using the AMP will require installing the passive speakers, and drilling a hole into your home for wiring to an AMP somewhere in the interior of your home. Unless your home is prewired, this can be a difficult task.
Ease of Use - Advantage AMP
The AMP barely has the edge here. Once your setup, all you need is the Sonos app to operate. With the MOVE, you also have to physically move the speaker outside when you want to use it.
Flexibility - Advantage MOVE
With the MOVE, you can place the speakers in various locations as needed, while the passive speakers with the AMP are in fixed locations.
Voice Control - Advantage MOVE
The MOVE has voice control on board while the AMP does not. In order to voice control, you would need to bring out an echo dot or Google mini with you (and plug in), or use voice through your phone. From my personal experience, echo dot's are not built for outdoor use, and do not pick up audio as well, and do not provide Alexa response nearly as clearly as the MOVE does.
TV Audio - Advantage AMP
The Sonos AMP has an HDMI-ARC port so that you can connect the TV directly to the AMP, while the MOVE does not.
Expand-ability - Advantage AMP
If you ever have a desire to add additional speakers to your outdoor setup, that's more easily done with an AMP. Adding more speakers with a MOVE strategy means more speakers to keep charged and move outside every time you want to listen to music, while additional speakers with the AMP (an extra pair without adding another AMP or speaker switch) is a more permanent option. That said, you can use existing speakers with an AMP and supplement the space with a MOVE as needed.
Wifi - Advantage MOVE
This is going depending on the particular home and what phone you're using, but from my experience, the MOVE can pickup a wifi signal from a farther distance than even your phone. This means that the MOVE can operate on voice control where your phone isn't available to control a Sonos AMP. And of course, the MOVE can switch to BT where WiFi isn't available.
Durability - Advantage AMP
The Sonos AMP is going to be well protected inside your home, with speakers built for outdoors exposed to the elements. When the speakers eventually fail, they are likely cheaper to replace than a single MOVE. The MOVE is pretty rugged, and can be moved inside during bad weather, but the fact is that it will be moved around a lot leaves it more exposed to damage, and the battery will eventually need to be replaced. It's worth noting though that passive speakers will fail suddenly leaving you without. The MOVE battery will gradually lose run time, giving you forewarning that replacement is needed.
Ownership - Advantage MOVE
One other factor to consider is that speakers with the AMP will need to be attached to your home. This may not be allowed if you renting your home. If you own your home, it's typical that anything that is physically attached to the home is a part of the home and cannot be take with you when you move out.
Project Appeal - Advantage AMP
This may seem like sort of an odd one, but if you're the type of person that takes pride in projects around the house...the MOVE is just too easy to setup. It's not going to give you quite the satisfaction of drilling holes in your house and installing speakers.
Single Use Time - Advantage AMP
The MOVE will eventually need to have battery charged, while the AMP will run indefinitely, This may not be an issue depending on your intended use, or if you can plug in with a USB charger without issue, but the AMP setup doesn't have this limitation.
Disturbing the Neighbors - Advantage MOVE
Passive speakers are usually attached under the eaves of the home, as they are easy place to mount speakers and the eaves help protect the speaker from the elements. Unfortunately, this means the speakers facing the neighbors yard and will often need to be played louder to reach your desired listening area. In contrast, the MOVE can be placed anywhere, facing away from neighbors and nearer to the listening area to reduce volume requirements. Passive speakers can be placed in the yard facing in ward, but that typically requires more installation work and exposes the speaker more to weather, increasing chance of failure.