Both choices seem acceptable.
I'd tend towards the RJ11 solution and use 6P6C for flexibility unless you were absolutely certain no extra facilities would be needed subsequently.
Both systems run the risk of other equipment being plugged in by careless users in an uncontrolled environment.
Cannon a.k.a. XLR connector (see below) is a superb solution if you need the robustness.
Stereo audio cable has the advantage of shielded balanced pairs being available if desired. While I'd expect a 10 metre cable length to be no problem in a benign environment, the shielding is a bonus in severe environments. Balanced pair is less of an issue as you will be using an unbalanced against ground data circuit. Reasonable cost. Cables are available that stand up well to use as a flexible lead. 4 pole versions are available. Connectors tend to short momentarily on insertion and removal - not usually an issue but worth noting. Some risk of connector damage from ham fisted users.
"RJ11" 6P4C or 6P6C cable and connectors has the advantages of low cost, good availability, balanced pairs, additional pair for "something else that turned out to be handy" if 6P6C is used. (Even 6P4C gives an extra wire (unbalanced against ground) for "other use". Cable is designed for use as a flexible cord within reason so is damage resistant. Current carrying capability is reasonable (not a major issue here). Shielding not usually provided. Locking tab connectors. Cheap versions prone to lock tab damage but otherwise resistant to user abuse. Versions can be had which allow pullout without damage - cheaper versions tend to break locking tabs off if abused. Not so good for inline connections usually (but parts are available if this is required).
Nothing stands out except perhaps Cannon microphone connectors.
"Cannon" a.k.a. XLR*: Possibly the most professional solution at a reasonable price if robustness matters. 3 pin and ground and higher pin count versions. Larger connectors than RJ11 or 3.5mm. Connectors available from cheap plastic with modest robustness to reasonably priced near bulletproof full-metal-jacket versions. Latchable. Can use variations on shielded or unshielded cable
6.5mm microphone connectors. Very available. Good prices. Larger connectors. Various number of poles. More user damage resistant than 3.5mm. (The photo below actually shows adaptors but the plug barrels are the same.)
Video cable with DB15 connectors. Thicker, more expensive. Available premade in various lengths to beyond 10m. Some shielded pairs or whole cable may be shielded. Quality connector. Larger connectors. Not usually good for inline connection.
Mini-DIN and similar: Small. Dearer. Damage prone. More connections but no real advantage.
Std DIN. Larger. Less damage prone. More connections but no real advantage.
Cannon / XLR:
"The XLR connector was invented by James H. Cannon, founder of Cannon Electric in Los Angeles, California (now part of ITT Corporation), and for this reason it is sometimes colloquially known as a cannon plug or cannon connector.
Originally manufactured as the Cannon X series, subsequent versions added a latch (Cannon XL) and then surrounded the female contacts with a resilient polychloroprene, which resulted in the part number prefix XLR
Source - Wikipedia.