I would like to know whether cells having both chloroplast and mitochondria organelles actively respire or the cells that lack chloroplast respire more.
I do not think that chloroplasts respire because it lacks terminal cytochrome oxidase. Therefore,a cell can respire more or less depending on the availability of carbon source. The presence or absence of chloroplasts in a cell does not matter
I have measured respiration and ATP production in thalli of Marchantia polymorpha L, a liverwort, when I did my PhD thesis in Plant Physiology. The liverwort has a dichotomous thallus which forms a gradient of old tissues on its base over middle aged tissue to the youngest tissues on the (growing) top of the thalli. Respiration is highest in the youngest tissue at the thalli tops, as well as ATP production.
For Phaseolus vulgaris L. grown in darkness, respiration is the highest in the hook of 8 day old etiolated plants. The hook happens to contain the youngest and actively dividing cells and tissues of the etiolated plant. Hence for a moss as well as a higher plant it seems that energy metabolism is most intense in the youngest tissues. I figger that this is not surprising. The more growth, the more energy required to sustain it.
There are exceptions however to this rule. In fruit - typically apples - a climacterium occurs during ripening. A climacterium is a rise in respiration in some fruits. The climacterium occurs when polymer sugars are degraded into dimer and monomer sugars. The energy required to perform the hydrolysis of sugar polymers is provided by an increase in respiration and hence energy production. Hence for some plant species their fruits respiration is maximal when the tissues reach the full ripening phase.
I think the phenomena I described occur pretty generally for many plants species. For fruits it might be more species dependent.
In tissues that are complex arrangements of reserve and transport to oxidation targets there are cases of intense thermogenic 'respiration' which depend on mitochondria, but are Alternative OXidases, cyanide resistant. Even if Arum italicum spadix is quite a sport it rose research from Lamarck to James and Beevers in the 50s and to recent times. This tissue has got very intense respiration, never saturates with O2 and its temperature can increase to more than 10°C above ambient. No cytochrome oxidase is involved. The spadix is really low in photosynthesis. The question on how photosynthesis modulates respiration inside a cell involves also peroxysomes and photorespiration, but probably your question is adequate only for single cells like microalgae taken either in autotrophy or in total heterotrophy, but they do not look like. In leaves fruits and roots there are transport, storage, breakdown and relative feedbacks, but energy fluxes on per cell basis can be higher or lower with or without chloroplats in darkness. In any case the sink intensity is an adeguate keyword in place of respiration, I guess.
I think photo respiration should not be equated with normal respiration. Similarly climacteric respiration in fruits. The respiration during the catabolic process in cells with and with out chloroplasts should be considered in my opinion
Photo respiration should not bee quoted with normal respiration. Similarly, climacteric respiration as well in fruits. Catabolic respiration of cells with and with out chloroplasts should be substantiated . Probably, the rate of respiration depends on the energy need of the cell. In fact, lot of ATPs can be generated in a cell with chloroplasts through photo phosphorylation, lessening the business of energy production by mitochondria through oxidative phosphorylation. On the other hand, the energy need of a cell devoid of chloroplasts is totally borne by the mitochondria
COX and AOX are respiration indeed mitochondrial. C2 respiration for depleting Rubisco oxygenase glycolate has got measurable quotient and I think is too respiration as it is driven by the same organelles on glycine after peroxisomes. I guess Arum is about the mot intense case but is AOX and very limited in time and relevance. My answer is then in storage tissues upon activation depending on signalling we observe very intense metabolic respiration far higher than the one measurable in photosynthetic tissues in darkness.