Both approaches are legitimate; they simply suit different rugs. The deciding factors are value, fibre, construction and how contaminated the rug is.
The honest summary is that on-site cleaning is convenient and limited, while off-site cleaning is thorough and slower.
On-site cleaning
The rug stays where it is, cleaning is quick and cost is lower. Limitations are real: dry soil deep in the foundation cannot be fully removed, rinsing is restricted, and drying happens in your room rather than under controlled conditions.
It suits robust, low-value or lightly soiled rugs, and situations where a rug genuinely cannot be moved.
Off-site cleaning
A specialist facility allows proper dusting, immersion or controlled washing, thorough rinsing and monitored flat drying. Both faces can be treated and fringes handled separately.
For wool, silk, hand-knotted, antique or urine-contaminated rugs, this is the responsible choice.
Deciding
Consider replacement value and sentimental value first. If losing the rug would matter, the controlled process is worth the wait.
Pet contamination in particular needs full rinsing to remove urine salts, which is very difficult to achieve on a floor.