Aims. We study the distant dust environment of two Long Period Comets: C/2003 O1 (LINEAR) (observed at $r_{\rm h}$ = 7.39 AU) and C/2004 K1 (Catalina) (observed at $r_{\rm h}$ = 3.43 AU). The case of C/2003 O1 is particularly interesting since the comet has a quite large perihelion heliocentric distance ($r_{\rm h}$ = 6.85 AU).Methods. We analysed $R$-band images taken at the CAHA 2.2 m telescope to characterise the properties of the cometary dust coma. The images of both comets were also used as input into an inverse numerical model, to derive information about the dynamical parameters of coma dust grains until a time ~500 days before the observation.Results. Both the comets appeared to be active, and of similar shape and size despite the great difference in their heliocentric distance of observation. C/2003 O1 exhibited a tail extending to at least 3.7 $\times$ 10$^5$ km. It is a very active object, since its Af$ρ$ is 552 $±$ 36 cm within the inner 5”. C/2004 K1 showed a similar long tail, extending to 2.6 $\times$ 10$^5$ km. Its Af$ρ$ is 539 $±$ 35 cm within the inner 5”. An almost constant dust grain ejection velocity between 0.5 and 0.9 m/s at 1 cm dust size has been derived for C/2003 O1 and an increase from 0.5 to 2 m/s at 1 cm dust size for C/2004 K1, reflecting the different volatile dragging the dust environment (probably CO for C/2003 O1 and water for C/2004 K1). Model results allow some speculations about the comet nucleus size of C/2003 O1 (LINEAR) and its CO content: for a $Q_{\rm CO}$ similar in value to those observed for other distant cometary objects, a comet radius $R_{\rm n}$ from 13 to 17 km can be inferred.