= Solution
The common one-per-cent <exoplanet transit depth> gives $R_p=0.1R_\star$. Apply the supplied <main-sequence mass-radius relation>, $R_\star/R_\odot=M_\star/M_\odot$, and <Kepler's third law>, neglecting the planet <mass>. For $P=6$ days,
$$
\begin{array}{c|c|c|c}
M_\star/M_\odot&a/\mathrm{AU}&R_p/R_\oplus&t_{\rm tr}\text{ (central)}\\\hline
1&0.0646&10.9&3.30\,\mathrm h\\
0.1&0.0300&1.09&0.711\,\mathrm h
\end{array}
$$
The companions are approximately Jupiter-sized and Earth-sized respectively; these are sizes, not independently determined <masses>. The duration uses the small-planet chord approximation. Counting the finite planet radius would increase first-to-fourth-contact durations by about ten per cent for central transits.
For equal distance, passband, cadence and noise dominated by stellar photon counting, the supplied <mass-luminosity relation> makes the solar-mass host about $10^3$ times more luminous, with a transit about $4.64$ times longer. At equal fractional <exoplanet transit depth>, signal-to-noise per event scales as $\delta\sqrt{\dot N_\gamma t_{\rm tr}}$, favouring the solar-mass host by about $\sqrt{1000\times4.64}\simeq68$. Equal apparent brightness would remove the luminosity advantage but retain the duration advantage. Without distances and noise properties the relative detectability is conditional. Transit probability is also larger for the solar-mass case, about $7.2\%$ versus $1.55\%$.
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